What would have been the implications if an eastern empire, like the Persians, were able to expand into Europe during the ancient or classical ages?

I'm reading Theodor Mommsen's History of Rome and he says cities were an important part of the Greek and Roman rule, while people in the Eastern kingdoms, before Hellenization, were dispersed throughout the countryside. The Romans, who considered themselves the protectors of Hellenization and the successors of Alexander, forced the Asians under their rule to congregate in cities, perhaps primarily as a means of control. But the result was more urbanization. Perhaps if things had worked the other way there would have been less urbanization in Greece and Rome, but it's hard to say, since the Greeks and Romans were extending their system to the East, and the Eastern rulers might not have disturbed the system already present in Europe.

Edit: On second thought, this post might be more appropriate for r/HistoricalWhatIf.